1. Field of the Invention
The present invention relates to an arrangement for calibrating a mechanical property of cantilevers, such as cantilevers for scanning probe microscopes and micro indentation devices.
The present invention further relates to a scanning probe microscope including such an arrangement.
The present invention further relates to a method for calibrating a mechanical property of such cantilevers.
2. Related Art
Scanning probe microscopes (SPM), such as atomic force microscopes s are widely used for the physical characterization of materials and devices when high spatial resolution and small feature sizes are of interest. SPMs are primarily used in imaging modes to provide topographic information, but they can also record the force interaction between a sensor tip of the cantilever and a sample.
Measuring the force interaction between the tip and surface involves measuring the deflection of a spring suspension. In the case of an SPM, the force sensor itself usually is a micro-fabricated cantilever that functions as a passive mechanical sensor. The micro-fabricated cantilever typically comprises a substrate layer, such as a silicon layer or a silicon nitride layer that is provided with a cover layer having a high reflectance, such as gold or aluminum. The deflection of the cantilever is typically determined by measuring the position to which a laser beam impingent on this cover layer is reflected. A force acting on the cantilever can then be calculated provided that a spring constant of the cantilever is known. However, process non-uniformities and variations during fabrication of the cantilever, contaminations and imperfections lead to uncertainties in cantilever's spring constant. Therefore, a calibration of the cantilevers is essential to enable reliable measurements. Similar probes are used in other instruments, such as indentation machines.
It is noted that SHEN SHENG ET AL disclose in: “Thermal conductance of biomaterial microcantilevers”, APPLIED PHYSICS LETTERS, MP, AMERICAN INSTITUTE OF PHYSICS, MELVILLE, N.Y., US, vol. 92, no. 6, 13 Feb. 2008, pages 63509-63509, D1 how the effective thermal conductance of a cantilever and the temperature at the tip of the cantilever can be determined by measuring the bending of the cantilever in response to two different thermal inputs: power absorbed at the tip and ambient temperature.
Furthermore it is noted that COOK S M ET AL compare two measurement methods in: “Practical implementation of dynamic methods for measuring atomic force microscope cantilever spring constants”, NANOTECHNOLOGY, IOP, BRISTOL, GB, vol. 17, no. 9, 14 May 2006, pages 2135-2145. The two measurement methods of atomic force microscope cantilever spring constants (k) compared therein are the thermal noise and Sader methods. Cook et al. select these methods for comparison as they are considered commonly applicable and relatively user-friendly, providing an in situ, non-destructive, fast measurement of k for a cantilever independent of its material or coating.
According to the thermal noise method the spring constant is calculated from the temperature T of the cantilever and the corresponding thermal vibration spectrum